Poisson--Lie contractions and quantum (1+1) groups

A. Ballesteros; F. J. Herranz; M. A. del Olmo; M. Santander

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Poisson--Lie contractions and quantum (1+1) groups

A. Ballesteros, F. J. Herranz, M. A. del Olmo, M. Santander

High Energy Physics - Theory · Submitted 30 Mar 1994

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim A Poisson--Hopf algebra of smooth functions on the (1+1) Cayley--Klein groups is constructed by using a classical $r$--matrix which is invariant under contraction.

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arXiv IDhep-th/9403182 (version 1)

Pith ID6PIL3D4T, Pith's permanent record of this paper and its review

CitationA. Ballesteros, F. J. Herranz, M. A. del Olmo, M. Santander. "Poisson--Lie contractions and quantum (1+1) groups." arXiv:hep-th/9403182 (1994). https://pith.science/paper/6PIL3D4T

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

A Poisson--Hopf algebra of smooth functions on the (1+1) Cayley--Klein groups is constructed by using a classical $r$--matrix which is invariant under contraction. The quantization of this algebra for the Euclidean, Galilei and Poincar\'e cases is developed, and their duals are also computed. Contractions on these quantum groups are studied.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A Poisson--Hopf algebra of smooth functions on the (1+1) Cayley--Klein groups is constructed by using a classical $r$--matrix which is invariant under contraction.	contribution 0.91	0.88	0.25	asserted 1.00
s1	The quantization of this algebra for the Euclidean, Galilei and Poincar\'e cases is developed, and their duals are also computed.	contribution 0.93	0.90	0.21	asserted 1.00
s2	Contractions on these quantum groups are studied.	contribution 1.00	0.82	0.12	asserted 0.84

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

A Poisson--Hopf algebra of smooth functions on the (1+1) Cayley--Klein groups is constructed by using a classical $r$--matrix which is invariant under contraction. The quantization of this algebra for the Euclidean, Galilei and Poincar\'e cases is developed, and their duals are also computed. Contractions on these quantum groups are studied.

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1 arXiv paper cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Builds on it 1 paper

This limit is achieved by generalizing the Lie bialgebra approach to quantum algebra contractions developed in [ref] to multiparametric Lie bialgebras and afterwards by introducing the contraction theory of universal $T$-matrices for the first time.

Universal $T$-matrices for quantum Poincar\'e groups: contractions and quantum reference frames · Concluding remarks · 0.80

Cites it as background 1 paper

We first recall the theory of Lie bialgebra contractions and Poisson–Lie groups which, based on previous results given in [ref] , was completely developed in [ref] .

Universal $T$-matrices for quantum Poincar\'e groups: contractions and quantum reference frames · Inönü–Wigner contractions of the universal T-matrix · 0.91

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